%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET677+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:36:48 AM UTC 2026
% Result : Theorem 0.14s 20.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 88 ( 27 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 96 ( 38 ~; 31 |; 10 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 40 ( 1 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,range(C,B,D))
& C = domain(C,B,D) ) ) ) ) ),
file('theBenchmark.p',p1) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(identity_relation_of(C),D)
=> ( C = range(B,C,D)
& subset(C,domain(B,C,D)) ) ) ) ) ),
file('theBenchmark.p',p2) ).
fof(p5,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
file('theBenchmark.p',p5) ).
fof(p34,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p34) ).
fof(prove_relset_1_44,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( subset(identity_relation_of(B),C)
=> ( B = range(B,B,C)
& B = domain(B,B,C) ) ) ) ),
file('theBenchmark.p',prove_relset_1_44) ).
fof(prove_relset_1_44_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( subset(identity_relation_of(B),C)
=> ( B = range(B,B,C)
& B = domain(B,B,C) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_44]) ).
fof(nnf_35,plain,
? [B] :
( ? [C] :
( ( range(B,B,C) != B
| domain(B,B,C) != B )
& subset(identity_relation_of(B),C)
& ilf_type(C,identity_relation_of_type(B)) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_44_neg]) ).
fof(sk_prove_relset_1_44_neg,plain,
( ( range(sK0,sK0,sK1) != sK0
| domain(sK0,sK0,sK1) != sK0 )
& subset(identity_relation_of(sK0),sK1)
& ilf_type(sK1,identity_relation_of_type(sK0))
& ilf_type(sK0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_35]) ).
cnf(c_62,negated_conjecture,
( range(sK0,sK0,sK1) != sK0
| domain(sK0,sK0,sK1) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_44_neg]) ).
cnf(c_63,negated_conjecture,
subset(identity_relation_of(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_44_neg]) ).
cnf(c_64,negated_conjecture,
ilf_type(sK1,identity_relation_of_type(sK0)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_44_neg]) ).
cnf(c_66,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p34]) ).
cnf(c_134,plain,
( ilf_type(B,relation_type(A,A))
| ~ ilf_type(B,identity_relation_of_type(A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p5]) ).
cnf(c_276,plain,
( ilf_type(A,relation_type(B,B))
| ~ ilf_type(A,identity_relation_of_type(B))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_66,c_134]) ).
cnf(c_135,plain,
( ilf_type(A,relation_type(B,B))
| ~ ilf_type(A,identity_relation_of_type(B)) ),
inference(resolve,[status(thm)],[c_66,c_276]) ).
cnf(c_144,plain,
( range(A,B,C) = B
| ~ subset(identity_relation_of(B),C)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p2]) ).
cnf(c_277,plain,
( range(C,A,B) = A
| ~ subset(identity_relation_of(A),B)
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_66,c_144]) ).
cnf(c_145,plain,
( range(B,C,A) = C
| ~ subset(identity_relation_of(C),A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_66,c_277]) ).
cnf(c_150,plain,
( domain(B,A,C) = B
| ~ subset(identity_relation_of(B),C)
| ~ ilf_type(C,relation_type(B,A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_278,plain,
( domain(A,C,B) = A
| ~ subset(identity_relation_of(A),B)
| ~ ilf_type(B,relation_type(A,C))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_66,c_150]) ).
cnf(c_151,plain,
( domain(B,C,A) = B
| ~ subset(identity_relation_of(B),A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_66,c_278]) ).
cnf(c_212,plain,
ilf_type(sK1,relation_type(sK0,sK0)),
inference(resolve,[status(thm)],[c_135,c_64]) ).
cnf(c_279,plain,
( domain(sK0,sK0,sK1) = sK0
| ~ subset(identity_relation_of(sK0),sK1) ),
inference(resolve,[status(thm)],[c_212,c_151]) ).
cnf(c_268,negated_conjecture,
domain(sK0,sK0,sK1) = sK0,
inference(resolve,[status(thm)],[c_63,c_279]) ).
cnf(c_280,plain,
( range(sK0,sK0,sK1) = sK0
| ~ subset(identity_relation_of(sK0),sK1) ),
inference(resolve,[status(thm)],[c_212,c_145]) ).
cnf(c_270,negated_conjecture,
range(sK0,sK0,sK1) = sK0,
inference(resolve,[status(thm)],[c_63,c_280]) ).
cnf(c_281,negated_conjecture,
( range(sK0,sK0,sK1) != sK0
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_268,c_62]) ).
cnf(c_282,negated_conjecture,
( sK0 != sK0
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_270,c_281]) ).
cnf(c_283,negated_conjecture,
sK0 != sK0,
inference(copy,[status(thm)],[c_282]) ).
cnf(c_275,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET677+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/20.38 % Computer : n002.cluster.edu
% 0.08/20.38 % Model : x86_64 x86_64
% 0.08/20.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/20.38 % Memory : 8046.5625MB
% 0.08/20.38 % OS : Linux 6.8.0-71-generic
% 0.08/20.38 % CPULimit : 300
% 0.08/20.38 % WCLimit : 300
% 0.08/20.38 % DateTime : Sat Sep 26 08:07:14 UTC 2026
% 0.08/20.38 % CPUTime :
% 0.08/20.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/20.38 % Process 1213591 was started by sandbox2 on n002,
% 0.08/20.38 % Sat Sep 26 08:07:14 2026
% 0.08/20.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/20.40
% 0.14/20.40 % From the command line: assign(max_seconds, 300).
% 0.14/20.43
% 0.14/20.43 % SZS status Theorem for theBenchmark
% 0.14/20.43
% 0.14/20.43 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/20.43 % Length of proof is 19.
% 0.14/20.43 % Level of proof is 5.
% 0.14/20.43 % Maximum clause weight is 25.000.
% 0.14/20.43 % Given clauses 60.
% 0.14/20.43
% 0.14/20.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------